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Three years after the state flung open the doors for municipalities to join its less costly health insurance program, not a single city or town now wants to come in.

The deadline for signing up for the Group Insurance Commission for 2011 passed this week with no takers — a disappointment for those who in 2007 believed state government had hit on a plan to save municipalities millions of dollars annually.

“This sends us back to the drawing board,’’ said Joel Barrera, deputy director of the Metropolitan Area Planning Council, a planning organization for 101 Boston-area communities, and a major proponent of the commission.

Barrera said the experiences of the 31 municipalities and regional government units that have joined the commission since 2007 clearly demonstrate the potential for substantial savings — an estimated $53 million a year collectively.

“We know the GIC saves millions of dollars, but we also know municipalities are not able to get the GIC,’’ he said. “That means we need a legislative fix.’’

The obstacle to joining for most municipalities is a provision in the law that requires them to get the approval of 70 percent of a panel of local union representatives.

Jay Gonzalez, Governor Deval Patrick’s secretary of administration and finance, said containing health care costs is one of the highest priorities as Patrick prepares for a second term. But while some sort of fix is needed, the GIC may not work for everyone, he said.

Gonzalez said the administration supports a bill to roll back that requirement to 50 percent.

“That would be meaningful change by reducing the barrier to the GIC,’’ he said.

Patrick and the state Legislature cooperated in 2007 in making the GIC an option for municipalities, which have been strapped for cash because of the rapidly escalating cost of providing health care coverage to employees, retirees, and elected officials.

Compared with municipalities, the GIC historically experienced lower cost increases. One factor was its size — it is the largest group insurer in the state — giving it greater bargaining power with providers.

But its ability to increase employee copayments and deductibles without union negotiations has also allowed the commission to shift some costs to plan participants.

Municipal unions, wary of higher out-of-pocket expenses for its members, have balked at efforts to move into the GIC.

A spokesman for House Speaker Robert A. DeLeo, Seth Gitell, called it “very disappointing’’ that no new municipalities signed up to move into the GIC and said lawmakers would address the municipal health care insurance crisis in the legislative session that begins next month.

David Falcone, a spokesman for Senate President Therese Murray, said “The GIC isn’t the answer for every town, but it’s an issue we’ll certainly continue to look at and work with the House and governor to see what’s best.’’

Dolores Mitchell, executive director of the GIC, said the fact that no communities plan to join next year was not a surprise.

“We are in a period of great uncertainty concerning health care insurance, and I think a lot of communities are treading water and waiting to see what happens next,’’ she said.

Last February, the GIC, facing a budget deficit, increased its deductibles in the middle of the fiscal year.

Mitchell said she thought that increase probably dampened interest in the GIC among some municipalities.

In the first two years after the GIC was available to cities and towns, about a dozen municipalities or other government units joined the state program annually. But last year Brookline and Hopedale were the only municipalities to join.

The Massachusetts Municipal Association, which lobbies on behalf of cities and towns, pressed hard last spring on Beacon Hill for passage of bills that would make it easier for municipalities to go into the GIC or give have the ability to increase copayments and deductibles without union negotiations.

Ultimately, municipal employee unions, citing the sanctity of collective bargaining, fought off such initiatives and the state Legislature abandoned further efforts.

Fed up with the lack of movement on Beacon Hill, Mayor Thomas M. Menino of Boston last month said he would attempt to create a city insurance commission, with the same kind of flexibility as its state counterpart. Such a course would require votes of the City Council and state Legislature.

Menino said if he gained the ability to increase copayments and deductibles the way the state GIC does the city could save $1 million a month. Currently, the city spends about $300 million for health care insurance, more than the Police Department’s entire budget.

Menino said he also supports a statewide referendum on the issue, which would ask voters directly to approve a change in state law allowing cities and towns to increase copayments and deductibles unilaterally.